Abstract
The Binary Mechanics Lab (BML) Simulator v3.13 was used in Random Mode to demonstrate the Hall effect in a cubic volume. Analysis of charge displacements of 1-states revealed the role of the proton cycle as the primary mechanism producing the Hall effect. This Hall effect demonstration and description of its mechanism further establish the heuristic value of binary mechanics postulates and equations.
Introduction
In 1879, Edwin Hall discovered that an electric current produced a transverse voltage in a conductor [1]. In Random Mode, the BML Simulator records displacements of positive and negative fractional charges, associated with the proton and electron cycles respectively [2], for each application of the binary mechanics (BM) update to the Schrödinger equation (eq. 17 in [3]).
Fig. 1: Proton 1-state Displacments
Abstract and Introduction
Proton size is presently estimated by measurements of proton charge radius of approximately 0.84 fm. In contrast, based on binary mechanics postulates and equations [1], reported proton radius is about 1.34 fm. This substantial size discrepancy may be resolved by data indicating that the proton charge radius may underestimate proton size because three parts of proton structure contain concentrations of positive fractional charges.
Fig. 1: Proton (Hadron) Structure and Cycle
[Updated: Aug. 24, 2025]
Abstract
A frequently asked question is, "How did binary mechanics (BM) derive the primary and secondary physical constants?" A true derivation of a "fundamental constant" value is based on first principles alone, without any use of other fundamental constants, which are really unexplained measurements. First, measured values of the so-called fundamental constants were reverse engineered to obtain values for the BM primary constants based on full quantization of energy, space and time, expressed in kg, meters and seconds respectively, which map directly to the SI units of measurement used in science. Second, the primary constant values, dubbed the Keene scale, were used to calculate the measured values of the previously unexplained secondary or "fundamental" constants.
Fig. 1: Physical Constant Derivation Highlights
Abstract
The three-quanta threshold for particle formation [1] and the mechanism of particle motion [2] are reviewed showing how these discoveries provided a basis for a new law of motion in physics [3].
Road to the Law of Motion
In 1994, the "Binary Mechanics" paper presented full quantization of energy, space and time, with equations for system state and its time development, without input from, or use of, any "unexplained measurements", wrongly known as "fundamental constants". "Binary Mechanics" (BM) was published in JBinMech in 2010 [4].
Fig. 1: Electron Cycle
Abstract and Introduction
The proton (hadron) bit cycle was rendered in a 3D animation illustrating features of the binary mechanics (BM) model of space [1] [2] and proton structure, discovered in 2011 [3] [4] and used in the first-ever derivation of Planck's constant from first principles of quantum theory in 2018 [5].
Fig. 1: Proton Bit Cycle Viewed Along Spin Axis
Legend: Spheres, 42 bit loci in matter d quark (dark red, green, blue), anti-matter d quark (light red, green, blue) and positron (grey) spot types. Brown bars, route of quanta in the proton cycle. Axis lines, X (blue), Y (pink) and Z (white) intersect at center of "home" spot cube, where the spin axis is approximately perpendicular to the page plane in this perspective.
Abstract and Introduction
Assertions that perfect vacuum and almost all of the volume of a single atom are "empty space" are questionable. In a replication of a previous simulation experiment [1] with additional analysis, perfect vacuum was defined as total energy density minus electron and nucleon particle density. Examining the entire range of non-zero energy quanta (1-state bit) densities, only about 12 percent or less of the quanta were associated with particles, indicating that perfect vacuum was composed of about 88 percent or more of quanta in the final state after cooling (Figs. 1 and 2). Threshold energy density for baryogenesis (nucleon formation) was 0.07 of maximum. In higher energy density initial states in the plasma and lepton-quark soup ranges, "explosive" centrifugal momentum leaves much lower particle and vacuum energy densities after cooling, which may be relevant to expanding universe questions.
Fig. 1: Vacuum Composition After Cooling to Zero Kelvin (Final Density)
[Updated: November 19, 2020]
Abstract and Introduction
Analysis of energy quanta distributions among spatial objects called spots [1] [2] revealed two quantum-level phenomena relevant to gravitation: dispersion and concentration of energy quanta (Fig. 1). First, in a lower energy density range, spots with multiple energy quanta dispersed, or lost, energy which was distributed to spots with initial lower, even zero, energy content. Second, at higher energy density, spots concentrated energy more than expected by random distribution. In brief, quantum analysis of spatial distribution of energy (and/or mass) identified two mechanisms which disperse or concentrate energy probably relevant to gravitational phenomena. A third mechanism was the effect of surface temperature on gravitation reported previously [3] [4] [5] [6]. The present results further integrate gravitation and space-time-energy quantization in binary mechanics and support a multi-factor treatment of gravity-related phenomena.
Fig. 1: Spot Energy Distribution vs Energy Density
[Updated: Nov 26, 2020]
Abstract and Introduction
Binary mechanics (BM) predicts the exact composition of protons and neutrons with maximum energy content but zero motion at zero degrees Kelvin. In this configuration, sequential loci in the proton and electron bit cycles are filled with alternating 0- and 1-state bits (Figs. 2 and 4) because zero motion requires absence of adjacent energy quanta pairs in the cycle sequence. Bit function analysis of particle composition after cooling to zero Kelvin completely confirms this hypothesis (Fig. 3). Results further illustrate how bit function analysis methodology may continue to support the leading position of Binary Mechanics Lab (BML) in advanced particle physics research.
Fig. 1: Spot Unit, Spot and Spot Cube
Abstract and Introduction
Planck's constant h was derived for the first time from first principles, based on the intrinsic proton spin in the proton bit cycle, confirming the derivation based on the electron bit cycle (Fig. 1 from [1]) [2]. A new method to derive h and the intrinsic electron spin based on summation of 1-state bit motion components of the total angular momentum was applied to the proton bit cycle to sum its angular momentum components. Results confirm (1) binary mechanics (BM) [3] postulates including the physical interpretation of BM space [4] and the time-development bit operations underlying the fundamental forces [5] which create the proton and electron bit cycles themselves and (2) the victory of Binary Mechanics Lab (BML) in the century-long physics grand championship race to derive constants from first principles of a coherent, comprehensive physical theory (BM) [6].
Fig. 1: Proton and Electron Bit Cycles
Legend: Six 1-state bit positions in electron cycle (yellow). 42 1-state bit positions in proton cycle. Matter d quarks (dark red, green, blue); anti-matter d quarks (light red, green, blue). Positron positions (gray). Arrows (purple) indicate bit motion direction and results of the strong bit operation. The unconditional bit operation (black) accounts for all motion between color-coded spot types. XYZ positions shown without commas: e.g., 013 is {0,1,3}.
[Updated: June 19, 2020]
How is binary mechanics different from quantum mechanics (QM)?
Legacy QM and General Relativity (GR) utilize continuous space-time theory, while binary mechanics (BM) [1] quantizes both space and time leading to definition of fundamental length L and time T constants. Recall that Planck's constant is an energy-time product (Jsec), not energy quantization per se. BM quantized energy as a 1-state bit (energy quanta) in a size L bit locus cube, expressed as M in kg. In short, BM quantizes the three units of measurement (Fig. 1 from [2]) and defines the system state bit function as a spatial pattern of 1- and 0-state bits [3].
Further, with space-time-energy quantization, infinitesimal time-evolution operators in legacy QM -- e.g., Standard Model (SM) math -- are not applicable since only integer increments are allowed. Hence, four bit operations [4] were based on a pair of relativistic Dirac spinor equations of opposite handedness including electromagnetic field components (Fig. 3 from [5]). In sum, both system state and time-development in BM is full QM, while SM math is partial QM. BM is complete QM, while SM math is incomplete QM.
Fig. 1: Century-Long Race Finish: Derivation of Constants From First Principles
Abstract and Introduction
Previous work has shown that quanta in the proton and electron bit cycles [1] moved in the same direction under applied magnetic potential fields regardless of the opposite net electric charge of the two quanta groups [2] [3]. This report looked at the effects of an applied electric potential field in either of two directions along the Y axis. Proton and electron cycle quanta moved according to their electric charge as expected from Coulomb's law. Also, both M and L type quanta participate in coding future motion. These findings further demonstrate that the bit function (eqs. 2 and 39 in [4]) in binary mechanics (BM) contains simultaneous position and motion representation.
Fig. 1: Proton Displacement In Electric Fields
Abstract and Introduction
Previous work has shown 1) object displacement after magnetic pulse injections [1] and 2) loss of motion-related inertia states after cooling to zero Kelvin [2]. These findings demonstrated that the bit function (eqs. 2 and 39 in [3]) in binary mechanics (BM) contains simultaneous position and motion representation. Therefore, the bit function is a major advance beyond the quantum mechanics (QM) wave function. Hence, the Heisenberg uncertainty principle has been demoted from fundamental QM precept to "observer effect". This paper replicates the particle motion study [1] adding separate tracking of energy quanta (1-state bits) in the oppositely-charged proton and electron bit cycles. Magnetic pulse injections displaced quanta regardless of electric charge, further supporting the notion that some or all L bits may represent magnetic monopoles. In sum, with eqs. 5 and 6 in [3], bit function M and L bits each have two types: plus or minus charge and right or left direction respectively.
Fig. 1: Proton Displacement After Magnetic Pulses
Legend: Pulses: L bits (Y^ up or Yv down) injected at Tick 0. In length constant L units,
displacement expressed as Y component minus mean(X,Z) translated to zero at Tick 0.
Abstract and Introduction
The postulates of binary mechanics (BM) [1] and physical interpretation of BM space [2] define fluxes of 1-state bits between spot units of particles of eight elementary types. Interparticle flux sequences define all possible particle motion events. In sum, the spot cube precisely defines 1) lepton-quark transitions, 2) quark-antiquark transitions, 3) the lepton motion mechanism, 4) lepton-mediated proton motion and 5) proton motion mediated by quark-antiquark transitions (Fig. 1). These interparticle flux and particle motion events form a tree which may be extended to define all possible particle interactions based solely on first principles.
Fig. 1: Discoveries in Particle Flux and Motion Analysis
[Updated: May 16, 2018]
Abstract and Introduction
Breaking news: Binary Mechanics Lab (BML) announces the first-ever derivation of the proton-electron mass ratio (Fig. 1). The derivation depended only on first principles of the comprehensive, fundamental physical theory known as binary mechanics (BM) [1] [2], without use of any mathematical constants or physical constants based on experimental measurements. A major consequence of this milestone discovery is two operational definitions of mass: 1) a fundamental, invariant value as a function of electron mass me and 2) the observed proton mass which depends on energy (1-state bit) density.
Fig. 1: First-ever Proton-Electron Mass Ratio Derivation
[Updated: May 12, 2018]
Abstract and Introduction
The effect of the time-evolution bit operations on elementary particle states [1] was examined by comparing proportions of spot states for each particle (spot type) with expected proportions based on random distribution of 1-state bits. Results include: 1) reduced probabilities of absolute vacuum and 2) increased probabilities of selected spot states (M and L bit composition) for each particle type, replicating previous findings [2]. That is, the time-development bit operations alter system state (the bit function) by concentrating 1-state M and L bits in selections of specific spot states in each elementary particle (spot type). These data define 1) a specific role of the magnetic force (vector bit operation) in particle differentiation and 2) a possible operational definition of "magnetic monopoles".
Fig. 1: Expected and Observed Particle Probabilities, E = 0, 1, 2
Abstract and Introduction
The Binary Mechanics Lab (BML) software release for Bit Function Analysis (BFA) may mark a milestone particle physics methodology advance. Particle interactions and effects of various independent variables such as electromagnetic potentials may now be viewed and assessed directly thereby reducing reliance on operational definition from distant event detector outputs, as currently used at particle accelerator sites such as CERN. This article describes use of the BFA program and some preliminary results which suggest that electron and quark particles and their energy levels may now be rigorously defined through direct observation.
Fig. 1: Particle Physics Methodology Milestone
Abstract and Introduction
On Sept. 18, 2017, Cat 5 hurricane Maria destroyed Binary Mechanics Lab (BML), located in the Commonwealth of Dominica in the Caribbean West Indies windward islands. just as BML was emerging as the leading fundamental physics lab in the world (see e.g. [1] [2] [3]). For over six months, BML had no utility-supplied electric power and internet. At present, BML has been largely rebuilt. This article reviews upcoming BML activities, including research publications and software.
Fig. 1: Getting Started: Bit Function Analysis
Abstract and Introduction
Matter creation based on electron and proton counts was examined after a simulated volume cooled to zero degrees Kelvin as a function of initial energy density. Findings include (1) lowest matter creation occurred starting from maximum energy density (1.0) and "perfect vacuum" density (0.1), (2) greatest matter creation was produced when starting from 0.3 energy density and (3) the SUVF bit operations order produced the greatest matter creation, compared to the VSUF and SVUF orders.
Background
Studies using the boosted energies of the Large Hadron Collider at CERN may provide only a primitive, keyhole view of possible events in the entire energy density range from absolute vacuum to absolute maximum energy density. Absolute vacuum and absolute maximum energy density are consequences of quantization of space and energy in binary mechanics (BM) [1] aka "full quantum mechanics". Energy was quantized by limiting spatial objects called bit loci to 0-states or 1-states. Then, absolute vacuum could be defined as a volume with all 0-state bit loci [2]. Note that so-called "perfect vacuum" may contain up to about 10% 1-state bit loci and is therefore not "empty space" (e.g., [3]). At the other extreme, absolute maximum energy density is achieved with all bit loci in a volume in the 1-state. The BM system state, named the bit function, is the spatial distribution of 1- and 0-state bits. With space and time quantization, infinitesimal operators in "partial quantum mechanics" (QM) were not applicable mathematically. Thus, four bit operations -- unconditional (U), scalar (S), vector (V) and strong (F), were based on relativistic Dirac spinor equations [1] [4] implementing time-development of the system state. Since results depend on bit operations order, only one order can be physically correct [5].
Abstract and Introduction
Identified matter-antimatter asymmetry mechanisms have indicated that predominance of matter over antimatter results from ongoing processes in the present [1], not from events in the distant past in the early universe. With space-time quantization in binary mechanics (BM) [2], quantum mechanics (QM) time-development operators with infinitesimal increments in position or time were no longer applicable mathematically. Hence, four bit operations -- unconditional (U), scalar (S), vector (V) and strong (F), were defined based on relativistic Dirac spinor equations. Since results depend on bit operations order [3], a major research objective is to determine the one and only physically correct bit operations order. The present research question was: which bit operation orders favor matter creation in present real-time? This study found that VSUF, SVUF and SUVF orders produce matter creation (Figs. 1 and 2) and eliminated the USVF, UVSF and VUSF orders based on this criterion.
Fig. 1: Matter Creation: Electrons
Legend: 1-state bit density: probability a bit locus is in 1-state. Exp: expected based on random distribution of 1-state bits. SUVF, SVUF, VSUF: bit operations order. Red arrows: absolute maximum temperature (maximum S + V counts).
From first principles of binary mechanics (BM) [1], eight and only eight fundamental or elementary particles were derived, each occupying a spatial object named a spot in a spot cube defined from a projection of spinor components of a pair of relativistic Dirac equations of opposite handedness to the eight vertexes of a cube quantizing space [2]. Each vertex or spot was postulated to consist of three perpendicular spot units defined from the two real components of the quantum mechanics (QM) complex wave function, further restricted to 0 or 1 allowed values, quantizing energy. Properties of the eight fundamental particles were then derived from the modulo 2 parities of the integer {x, y, z} spot coordinates in the spatial lattice, including charge, color, matter vs antimatter status, unconditional bit motion direction, handedness (left or right helicity), etc (Table 1 in [1],). These properties were used to show how most Standard Model (SM) lepton and quark particles may be compositions of the eight BM elementary particles [3]. This article adds information on some mesons and baryons, further illustrating their composition from BM particles and how the "three generations of matter" arise naturally from this analysis.
Table 1: Generation 1: Some TWO-d Mesons
Legend: Generation by number of d quarks (TWO-d). r, red; g, green; b, blue. /, antiparticle. X*, spot units in neighboring spot cubes.
